It has been proved by the authors that the (extended) Sadowsky functional can be deduced as the Gamma-limit of the Kirchhoff energy on a rectangular strip, as the width of the strip tends to 0. In this paper, we show that this Gamma-convergence result is stable when affine boundary conditions are prescribed on the short sides of the strip. These boundary conditions include those corresponding to a Mobius band. This provides a rigorous justification of the original formal argument by Sadowsky about determining the equilibrium shape of a free-standing Mobius strip. We further write the equilibrium equations for the limit problem and show that, under some regularity assumptions, the centerline of a developable Mobius band at equilibrium cannot be a planar curve.

Stability of Boundary Conditions for the Sadowsky Functional

Maria Giovanna Mora;
2022-01-01

Abstract

It has been proved by the authors that the (extended) Sadowsky functional can be deduced as the Gamma-limit of the Kirchhoff energy on a rectangular strip, as the width of the strip tends to 0. In this paper, we show that this Gamma-convergence result is stable when affine boundary conditions are prescribed on the short sides of the strip. These boundary conditions include those corresponding to a Mobius band. This provides a rigorous justification of the original formal argument by Sadowsky about determining the equilibrium shape of a free-standing Mobius strip. We further write the equilibrium equations for the limit problem and show that, under some regularity assumptions, the centerline of a developable Mobius band at equilibrium cannot be a planar curve.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1466848
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